A method for estimating the flocculation time of monodispersed sediment suspensions

A new method is presented for determining the flocculation time of monodispersed sediment suspensions. Flocculation time is the critical time at which abrupt changes in the particle size spectrum of an aggregative suspension occurs. This method predicts flocculation times to within 6% of values predicted by a geometric sectional aggregation model (Batterham, R.J., Hall, J.S. and Barton, G., 1981. In: Proceedings, 3rd International Symposium on Agglomeration, Nürnberg, Federal Republic of Germany, pp. A136–A150) but uses only a fraction of the computational effort. Flocculation times estimated in this way are superior to estimates of flocculation time scale made using half-life because particle geometry and differential settling encounter are taken into account. The proposed model is based on typical size distributions calculated using the Batterham et al. model. These size distributions have approximately equal mass in geometrically increasing size classes, i.e. they are Junge-dispersed. By assuming that the suspension remains Junge-dispersed throughout its evolution, the system of differential equations required to describe the suspension reduces to a single differential equation. Flocculation times are calculated for three values of maximum floc size (dmax={10,1,0.1 mm}), a maximum settling velocity of ws=1 mm s-1, and a variety of initial conditions. For a given set of inputs, flocculation times calculated in this way are linearly related to those calculated using the Batterham et al. model, but the slope of the relationship varies with fractal dimension. Multiple linear regression equations are developed to directly relate the two. The effect of including sinking losses into the Batterham et al. model is also investigated. If the sinking loss time scale is much longer than the flocculation time, then the suspension becomes flocculated at roughly the same time it would have had there been no sinking losses, and the new method can be used. Conversely, if the sinking time scale is less than or equal to the flocculation time, then the new method cannot be used.